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Bose Einstein Condensates in optical lattices under an external confinement are expected to form coexisting Superfluid and Mott-Insulating domains [1] reminiscent of the quantum phase transition for the infinite system [2]. The experimentally observed transition [3] is presently ascribed to relative shrinking/widening of the different domains. The presence of superfluid domains and the excitations of the interfaces between the two phases play a crucial role in the time evolution of the system under modulations of the parameters of the system as well as in its thermodynamic properties. In this work we derive the dispersion relation of the surface waves at the interfaces between Mott-Insulating and Superfluid phases. We then calculate their contribution to the heat capacity of the system and show how its low temperature scaling allows a direct experimental test of the existence and properties of Mott-Superfluid domains [4]. A further independent probe of the domains is considered studying the response of the system to a periodic modulation of the intensity of the optical lattice. The induced parametric resonances of the superfluid excitations are reflected in the energy absorption by the atomic cloud, yielding information about the structure of different domains [5]. [1] D. Jaksch et al. , Phys. Rev. Lett. 81, 3108 (1998) [2] M. P. A. Fisher et al. , Phys. Rev. B 40, 546 (1989) [3] M. Greiner et al. , Nature 415, 39 (2002) [4] E. Mariani and A. Stern, Phys. Rev. Lett. 95, 263001 (2005) [5] E. Mariani, L. Goren and A. Stern, to be submitted to Phys. Rev. Lett. |
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